Submodular Functions: We let \(\)  denote the ground-set of \(n\)  data points \(= \lbrace 1, 2, 3,...,n \rbrace \)  and a set function \(f:2^{} \xrightarrow{} \Re \) .
The function \(f\)  is submodular [1]} if it satisfies the diminishing marginal returns, namely \(f(j | ) = f(\cup j) - f() \ge f(j | )\)  for all \(\subseteq \subseteq , j \notin \) .
Submodularity ensures that a greedy algorithm achieves bounded approximation factor when maximized [2]}.
